Hazard curvature makes within-host variability costly for survival

Area of Science:

• Mathematical Biology
• Ecology
• Evolutionary Biology

Background:

• Within-host dynamics of tumors, pathogens, and immune responses are often modeled using ecological and evolutionary principles.
• However, clinically relevant outcomes focus on host survival rather than internal population dynamics.

Purpose of the Study:

• To develop a framework linking mechanistic within-host dynamics to host survival outcomes.
• To introduce the 'curvature principle' explaining how variability in host states affects mortality risk.

Main Methods:

• Developed a framework connecting within-host dynamics to host outcomes via a hazard map.
• Introduced the curvature principle, analyzing hazard functions and temporal variance.
• Extended the framework to proportional-hazards joint models, deriving a curvature penalty.
• Illustrated the theory with models of tumor dynamics, pathogen-immune interactions, and SARS-CoV-2 kinetics.

Main Results:

• The curvature principle states that variability in harmful host states increases cumulative hazard, especially when the hazard function is convex.
• A curvature penalty (½γ²·Varw(z)) quantifies the impact of variability on cumulative hazard.
• Demonstrated an endpoint mismatch where strategies optimizing burden metrics may worsen survival.

Conclusions:

• Hazard curvature is a key factor linking within-host dynamics, time-to-event outcomes, and treatment design.
• Variability in host state trajectories significantly impacts survival, necessitating consideration in clinical strategies.
• The developed framework provides a quantitative link between internal biological processes and patient outcomes.